Optical differential phase-shift keying (DPSK) has become an attractive modulation format that offers high receiver sensitivity and high tolerance to some fiber nonlinear effects such as cross-phase modulation and four-wave mixing. Several record-setting, long-haul, high-speed (≧10 Gb/s) optical fiber transmissions have been demonstrated using DPSK.
More recently, a family of optical DPSK referred to as optical Multi-chip DPSK (MC-DPSK) has been introduced. (See, e.g., M. Nazarathy et al., “Multichip differential phase encoded optical transmission,” IEEE Photon. Technol. Lett., vol. 17, no. 5, pp. 1133-1135, May 2005, hereinafter “Nazarathy”.) MC-DPSK has its origins in wireless communications. (See, e.g., D. Divsalar et al., “Multiple-symbol differential detection of MPSK,” IEEE Trans. Commun., vol. COM-38, no. 3, pp. 300-308, March 1990, hereinafter “Divsalar”.)
In MC-DPSK, multiple differential detections are performed over a window of multiple consecutive symbol intervals, also referred to as “chips.” A soft decision circuit is used to extract the transmitted data based on maximum-likelihood. As the number of chips increases, the performance of MC-DPSK approaches the performance of coherent detection PSK. (See e.g., Y. Yadin et al., “Soft detection of multichip DPSK over the nonlinear fiber-optic channel,” IEEE Photon. Technol. Lett., vol. 17, no. 9, pp. 2001-2003, September 2005, hereinafter “Yadin”; and Nazarathy.)
MC detection provides large receiver sensitivity gain for multi-level DPSK signals. (See Nazarathy and Divsalar.) For differential binary phase-shift keying (DBPSK), the MC detection gain is small (<0.5 dB) in the linear regime. (See Yadin.). The MC-DPSK gain can be enhanced in the nonlinear regime where nonlinear phase noise, resulting from the Gordon-Mollenauer effect, becomes the dominating penalty source. (See, J. P. Gordon et al., “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett., vol. 15, pp. 1351-1353, 1990.) Even with 3-chip detection, a sensitivity gain of over 1 dB can be obtained for DPSK.
Yadin describes a soft detection circuit for 3-chip DBPSK, such as that shown in FIG. 1. The circuit 100 comprises a differential detection circuit 110 and a soft decision circuit 120. As shown in FIG. 1, the Yadin soft decision circuit 120 requires several electrical summers (Σ) with high-speed analog inputs and outputs as well as a selector to select the largest summer output. The summers implement the following set of equations:q00=qT[k]+qT[k−1]+q2T[k], q01=−qT[k]+qT[k−1]−q2T[k], q10=qT[k]−qT[k−1]−q2T[k], q11=−qT[k]−qT[k−1]+q2T[k],  (1)
where qT[k], qT[k−1], and q2T[k], are three differentially detected signals based on comparisons between the k-th and (k−1)-th bit pair, the (k−1)-th and (k−2)-th bit pair, and the k-th and (k−2)-th bit pair, respectively. The variables q00-q11, referred to as “decision variables,” are indicative of the likelihood of the two-bit sequence represented by their indices. The soft decision circuit 120 determines (using the analog summers) the decision variables q00-q11, selects the largest decision variable, and outputs the two bits corresponding to the largest decision variable. A “hard” detection of DBPSK can be performed based on only the value of qT[k]. Soft detection, however, has been found to provide superior performance.
The analog soft decision circuit such as that described by Yadin has several drawbacks, including the fact that high-speed analog summers are quite technically challenging to make, and are not yet commercially available. In addition, selecting the largest decision variable from the four decision variables entails significant additional circuitry.